{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T12:54:41Z","timestamp":1791982481114,"version":"4.4.0"},"reference-count":28,"publisher":"PeerJ","license":[{"start":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T00:00:00Z","timestamp":1639958400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Mongkut\u2019s University of Technology North Bangkok","award":["KMUTNB-65-KNOW-09"],"award-info":[{"award-number":["KMUTNB-65-KNOW-09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Flash flooding and landslides regularly cause injury, death, and homelessness in Thailand. An advancedwarning system is necessary for predicting natural disasters, and analyzing the variability of daily precipitation might be usable in this regard. Moreover, analyzing the differences in precipitation data among multiple weather stations could be used to predict variations in meteorological conditions throughout the country. Since precipitation data in Thailand follow a zero-inflated lognormal (ZILN) distribution, multiple comparisons of precipitation variation in different areas can be addressed by using simultaneous confidence intervals (SCIs) for all possible pairwise ratios of variances of several ZILN models. Herein, we formulate SCIs using Bayesian, generalized pivotal quantity (GPQ), and parametric bootstrap (PB) approaches. The results of a simulation study provide insight into the performances of the SCIs. Those based on PB and the Bayesian approach via probability matching with the beta prior performed well in situations with a large amount of zero-inflated data with a large variance. Besides, the Bayesian based on the reference-beta prior and GPQ SCIs can be considered as alternative approaches for small-to-large and medium-to-large sample sizes from large population, respectively. These approaches were applied to estimate the precipitation variability among weather stations in lower southern Thailand to illustrate their efficacies.<\/jats:p>","DOI":"10.7717\/peerj.12659","type":"journal-article","created":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T04:31:10Z","timestamp":1639974670000},"page":"e12659","source":"Crossref","is-referenced-by-count":1,"title":["Multiple comparisons of precipitation variations in different areas using simultaneous confidence intervals for all possible ratios of variances of several zero-inflated lognormal models"],"prefix":"10.7717","volume":"9","author":[{"given":"Patcharee","family":"Maneerat","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Rajabhat Uttaradit University, Uttaradit, Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sa-Aat","family":"Niwitpong","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics, King Mongkut\u2019s University of Technology North Bangk, Bangkok,  Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"4443","published-online":{"date-parts":[[2021,12,20]]},"reference":[{"key":"10.7717\/peerj.12659\/ref-1","volume-title":"The lognormal distribution: with special reference to its uses in economics","author":"Aitchison","year":"1963"},{"issue":"14","key":"10.7717\/peerj.12659\/ref-2","doi-asserted-by":"publisher","first-page":"2684","DOI":"10.1002\/sim.3080","article-title":"Comparing the means and variances of a bivariate log-normal distribution","volume":"27","author":"Bebu","year":"2008","journal-title":"Statistics in Medicine"},{"key":"10.7717\/peerj.12659\/ref-3","volume-title":"Bayesian inference in statistical analysis","author":"Box","year":"1973"},{"issue":"2","key":"10.7717\/peerj.12659\/ref-4","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1080\/00401706.1984.10487938","article-title":"Confidence intervals on linear combinations of variance components in the unbalanced one-way classification","volume":"26","author":"Burdick","year":"1984","journal-title":"Technometrics"},{"issue":"6","key":"10.7717\/peerj.12659\/ref-5","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1016\/S0309-1708(98)00043-8","article-title":"On the estimation of radar rainfall error variance","volume":"22","author":"Ciach","year":"1999","journal-title":"Advances in Water Resources"},{"issue":"5","key":"10.7717\/peerj.12659\/ref-6","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1016\/j.jspi.2010.11.007","article-title":"One-sided confidence intervals for population variances of skewed distributions","volume":"141","author":"Cojbasic","year":"2011","journal-title":"Journal of Statistical Planning and Inference"},{"issue":"12","key":"10.7717\/peerj.12659\/ref-7","doi-asserted-by":"publisher","first-page":"5562","DOI":"10.1016\/j.csda.2007.03.023","article-title":"Nonparametric confidence intervals for population variance of one sample and the difference of variances of two samples","volume":"51","author":"Cojbasic","year":"2007","journal-title":"Computational Statistics & Data Analysis"},{"key":"10.7717\/peerj.12659\/ref-8","article-title":"Over 50,000 households hit by floods in south","author":"David","year":"2021","journal-title":"Technical report"},{"key":"10.7717\/peerj.12659\/ref-9","article-title":"Automatic weather system","author":"Department","year":"2021","journal-title":"Technical report"},{"issue":"2","key":"10.7717\/peerj.12659\/ref-10","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s10651-007-0046-8","article-title":"Confidence intervals for the mean of the delta-lognormal distribution","volume":"15","author":"Fletcher","year":"2008","journal-title":"Environmental and Ecological Statistics"},{"issue":"8","key":"10.7717\/peerj.12659\/ref-11","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1016\/j.jmva.2009.01.009","article-title":"Simultaneous credible intervals for small area estimation problems","volume":"100","author":"Ganesh","year":"2009","journal-title":"Journal of Multivariate Analysis"},{"key":"10.7717\/peerj.12659\/ref-12","volume-title":"Bayesian data analysis","author":"Gelman","year":"2014"},{"issue":"372","key":"10.7717\/peerj.12659\/ref-13","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1080\/01621459.1980.10477565","article-title":"Confidence intervals on nonnegative linear combinations of variances","volume":"75","author":"Graybill","year":"1980","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"10.7717\/peerj.12659\/ref-14","first-page":"261","article-title":"Simultaneous fiducial generalized condence intervals for ratios of means of lognormal distributions","volume":"35","author":"Hannig","year":"2006","journal-title":"Austrian Journal of Statistics"},{"issue":"6","key":"10.7717\/peerj.12659\/ref-15","doi-asserted-by":"publisher","first-page":"1294","DOI":"10.1016\/j.jspi.2011.12.006","article-title":"Bayesian confidence intervals for means and variances of lognormal and bivariate lognormal distributions","volume":"142","author":"Harvey","year":"2012","journal-title":"Journal of Statistical Planning and Inference"},{"issue":"3","key":"10.7717\/peerj.12659\/ref-16","doi-asserted-by":"publisher","first-page":"345","DOI":"10.2991\/jsta.2017.16.3.6","article-title":"Improved confidence intervals for the ratio of coefficients of variation of two lognormal distributions","volume":"16","author":"Hasan","year":"2017","journal-title":"Journal of Statistical Theory and Applications"},{"issue":"8","key":"10.7717\/peerj.12659\/ref-17","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1080\/00949655.2018.1439033","article-title":"Confidence intervals for the mean and a percentile based on zero-inflated lognormal data","volume":"88","author":"Hasan","year":"2018","journal-title":"Journal of Statistical Computation and Simulation"},{"issue":"5","key":"10.7717\/peerj.12659\/ref-18","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1080\/03610918.2011.552824","article-title":"Interval estimation for the difference of two independent variances","volume":"40","author":"Herbert","year":"2011","journal-title":"Communications in Statistics - Simulation and Computation"},{"issue":"4","key":"10.7717\/peerj.12659\/ref-19","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1080\/00949655.2016.1225742","article-title":"Simultaneous confidence intervals for comparing several inverse Gaussian means under heteroscedasticity","volume":"87","author":"Kharrati-Kopaei","year":"2017","journal-title":"Journal of Statistical Computation and Simulation"},{"key":"10.7717\/peerj.12659\/ref-20","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.spl.2015.07.002","article-title":"Parametric bootstrap simultaneous confidence intervals for differences of means from several two-parameter exponential distributions","volume":"106","author":"Li","year":"2015","journal-title":"Statistics & Probability Letters"},{"issue":"7","key":"10.7717\/peerj.12659\/ref-21","doi-asserted-by":"publisher","first-page":"1769","DOI":"10.1002\/bimj.201900079","article-title":"Bayesian confidence intervals for the difference between variances of deltalognormal distributions","volume":"62","author":"Maneerat","year":"2020","journal-title":"Biometrical Journal"},{"key":"10.7717\/peerj.12659\/ref-22","doi-asserted-by":"publisher","first-page":"229","DOI":"10.4310\/20-SII630","article-title":"Bayesian condence intervals for variance of delta-lognormal distribution with an application to rainfall dispersion","volume":"14","author":"Maneerat","year":"2021","journal-title":"Statistics and its Interface"},{"issue":"0","key":"10.7717\/peerj.12659\/ref-23","first-page":"1","article-title":"Bayesian confidence intervals for a single mean and the difference between two means of delta-lognormal distributions","volume":"0","author":"Maneerat","year":"2019","journal-title":"Communications in Statistics - Simulation and Computation"},{"issue":"7","key":"10.7717\/peerj.12659\/ref-24","doi-asserted-by":"publisher","first-page":"e0253935","DOI":"10.1371\/journal.pone.0253935","article-title":"Simultaneous confidence intervals for all pairwise comparisons of the means of delta-lognormal distributions with application to rainfall data","volume":"16","author":"Maneerat","year":"2021","journal-title":"PLOS ONE"},{"key":"10.7717\/peerj.12659\/ref-25","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.csda.2013.07.039","article-title":"Simultaneous confidence intervals for ratios of means of several lognormal distributions: a parametric bootstrap approach","volume":"69","author":"Sadooghi-Alvandi","year":"2014","journal-title":"Computational Statistics & Data Analysis"},{"key":"10.7717\/peerj.12659\/ref-26","article-title":"Flash update: no. 01 flooding, landslide and windstorms in southern Thailand, Thailand 11 January 2021","author":"Thailand","year":"2021","journal-title":"Technical report"},{"issue":"20","key":"10.7717\/peerj.12659\/ref-27","doi-asserted-by":"publisher","first-page":"3223","DOI":"10.1002\/sim.2169","article-title":"Inferences on the mean of zero-inflated lognormal data: the generalized variable approach","volume":"24","author":"Tian","year":"2005","journal-title":"Statistics in Medicine"},{"issue":"7","key":"10.7717\/peerj.12659\/ref-28","doi-asserted-by":"publisher","first-page":"1471","DOI":"10.1080\/02664763.2014.881780","article-title":"Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data","volume":"41","author":"Wu","year":"2014","journal-title":"Journal of Applied Statistics"}],"container-title":["PeerJ"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/peerj.com\/articles\/12659.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/peerj.com\/articles\/12659.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/peerj.com\/articles\/12659.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/peerj.com\/articles\/12659.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T04:31:27Z","timestamp":1639974687000},"score":1,"resource":{"primary":{"URL":"https:\/\/peerj.com\/articles\/12659"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,20]]},"references-count":28,"alternative-id":["10.7717\/peerj.12659"],"URL":"https:\/\/doi.org\/10.7717\/peerj.12659","archive":["CLOCKSS","LOCKSS","Portico"],"relation":{"has-review":[{"id-type":"doi","id":"10.7287\/peerj.12659v0.1\/reviews\/1","asserted-by":"object"},{"id-type":"doi","id":"10.7287\/peerj.12659v0.1\/reviews\/2","asserted-by":"object"}]},"ISSN":["2167-8359"],"issn-type":[{"value":"2167-8359","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,20]]},"article-number":"e12659"}}